Problem: Express your answer as a mixed number simplified to lowest terms. $10\dfrac{3}{4}-6\dfrac{5}{6} = {?}$
Answer: Find a common denominator for the fractions: $= {10\dfrac{9}{12}}-{6\dfrac{10}{12}}$ Convert ${10\dfrac{9}{12}}$ to ${9 + \dfrac{12}{12} + \dfrac{9}{12}}$ So the problem becomes: ${9\dfrac{21}{12}}-{6\dfrac{10}{12}}$ Separate the whole numbers from the fractional parts: $= {9} + {\dfrac{21}{12}} - {6} - {\dfrac{10}{12}}$ Bring the whole numbers together and the fractions together: $= {9} - {6} + {\dfrac{21}{12}} - {\dfrac{10}{12}}$ Subtract the whole numbers: $=3 + {\dfrac{21}{12}} - {\dfrac{10}{12}}$ Subtract the fractions: $= 3+\dfrac{11}{12}$ Combine the whole and fractional parts into a mixed number: $= 3\dfrac{11}{12}$